Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions

详细信息    查看全文

• 作者：Ruyun Ma^a ; ¹ ; ^{mary@nwnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Tianlan Chen^a ; ^{chentianlan511@126.com" class="auth_mail" title="E-mail the corresponding author} ; Haiyan Wang^b ; ^{Haiyan.Wang@asu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Radial eigenvalue ; Neumann problem ; Nonconstant radial solutions ; Bifurcation ; Perron&ndash ; Frobenius Theorem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 November 2016
• 年：2016
• 卷：443
• 期：1
• 页码：542-565
• 全文大小：433 K

文摘

Let lsi1" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16301913&_mathId=si1.gif&_user=111111111&_pii=S0022247X16301913&_rdoc=1&_issn=0022247X&md5=1ae759d167975db0d86de7bf20fdbaba" title="Click to view the MathML source">Bb>Rb>lass="mathContainer hidden">lass="mathCode">low="scroll">b>BRb> be the ball of radius R   in lsi2" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16301913&_mathId=si2.gif&_user=111111111&_pii=S0022247X16301913&_rdoc=1&_issn=0022247X&md5=5cf7f9ac3fbbad299a864af601681500" title="Click to view the MathML source">R^Nlass="mathContainer hidden">lass="mathCode">low="scroll">ble-struck">RN with lsi3" class="mathmlsrc">lass="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16301913&_mathId=si3.gif&_user=111111111&_pii=S0022247X16301913&_rdoc=1&_issn=0022247X&md5=f174e063c5921d90c548055b91cbefa1" title="Click to view the MathML source">N≥2lass="mathContainer hidden">lass="mathCode">low="scroll">N≥2. We consider the nonconstant radial positive solutions of elliptic systems of the form where f and g are nondecreasing in each component. With few assumptions on the nonlinearities, we apply bifurcation theory to show the existence of at least one nonnegative, nonconstant and nondecreasing solution.